## Thomas' Calculus 13th Edition

$5$
$\overrightarrow{AB} = \langle 1-0, 2-0,0-0 \rangle= \langle 1,2, 0 \rangle$ $\overrightarrow{AC} = \langle 0, -3, 2 \rangle$ $\overrightarrow{AD} = \langle 3, -4, 5 \rangle$ The volume of the parallelopiped is the absolute value of the triple scalar product, $( \overrightarrow{AB}\times \overrightarrow{AC})\cdot \overrightarrow{AD}=\left|\begin{array}{rrr} 1 & 2 & 0\\ 0 & -3 & 2\\ 3 & -4 & 5 \end{array}\right|=1(-15+8)-2(0-6)+0$ $=-7+12=5$ $V=|5|=5$